Final answer:
The correct answer is option C. To find the theater stage's actual area from the blueprint with the scale factor of 1 inch to 6 feet, we square the linear scale factor and multiply by the blueprint's area, resulting in an actual area of 1728 ft².
Step-by-step explanation:
The student's question involves finding the actual area of a theater stage using a given scale factor. The scale factor is 1 inch on the blueprint is equivalent to 6 feet on the actual stage. To find the actual area, we need to consider the scale factor's effect on both the length and width dimensions, which means squaring the linear scale factor because the area is two-dimensional.
The area of the stage on the blueprint is given as 48 square inches. Since the scale factor is 1 inch to 6 feet, the linear scale conversion is squared to get the area scale conversion: (6 feet/inch)² = (6 feet)² = 36 feet/inch². Therefore, we multiply the blueprint area by the area scale conversion: 48 in² × 36 ft²/in² = 1728 ft².
Thus, the correct answer to the student's question is 1728 ft², which corresponds to option C.